Question
4 Solve: \( \frac{5-6 a}{2}>3 \) You must use an a in your answer!
Ask by Li Hanson. in the United States
Jan 15,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( a < -\frac{1}{6} \)
Solution
Solve the equation \( \frac{5-6a}{2}>3 \).
Solve the inequality by following steps:
- step0: Solve for \(a\):
\(\frac{5-6a}{2}>3\)
- step1: Multiply both sides:
\(\frac{5-6a}{2}\times 2>3\times 2\)
- step2: Multiply the terms:
\(5-6a>6\)
- step3: Move the constant to the right side:
\(-6a>6-5\)
- step4: Subtract the numbers:
\(-6a>1\)
- step5: Change the signs:
\(6a<-1\)
- step6: Divide both sides:
\(\frac{6a}{6}<\frac{-1}{6}\)
- step7: Divide the numbers:
\(a<-\frac{1}{6}\)
The solution to the inequality \( \frac{5-6a}{2}>3 \) is \( a < -\frac{1}{6} \).
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Simplify this solution Extra Insights
To solve the inequality \( \frac{5-6a}{2} > 3 \), first multiply both sides by 2 to eliminate the fraction: \( 5 - 6a > 6 \). Next, subtract 5 from both sides: \(-6a > 1\). Now, divide both sides by -6, remembering to flip the inequality sign: \( a < -\frac{1}{6} \). So, the solution is \( a < -\frac{1}{6} \) or in interval notation: \( (-\infty, -\frac{1}{6}) \).
